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11 is the fifth prime number and the first 2-digit prime. 11's prime factors are 1 and 11.

Proofs

  • Yes — 11 can be divided by 1.
  • No — 11 cannot be divided by 2-10.
  • Yes — 11 can be divided by 11.
  • Therefore 11 has exactly 2 integer factors, 11 and 1.

As an Exponent of Mersenne Number

211 - 1, which is the number 2,047, can be factored into 23 x 89, and therefore not a prime number.

Relationship with other odd numbers

The numbers before

  • The previous odd number, 9, is a square number.
  • The odd number previous to 9 is 7. 7 is a prime number.
    • 7 and 11 are four numbers apart; therefore, they are cousin primes.
  • The odd number previous to 7 is 5. 5 is a prime number.
    • 5 and 11 are six numbers apart; therefore, they are sexy primes.

The numbers after

  • The next odd number, 13, is a prime number.
    • There are no odd numbers between 11 and 13. As a result, they are twin primes.
  • 15, the odd number following 13, is not a prime number. It is divisible by 3 and 5.
  • 17, the odd number following 15, is a prime number.
    • 11 and 17 are six numbers apart; therefore, they are sexy primes.

Trivia

  • 11 is part of a pattern of prime numbers in which the digits of a prime number can be added to create another prime number. In 11's case, its digits add to 2. 11 is also the sum of the digits of 29.
  • 11 is the only prime number that is 8 away from 2 different prime numbers (3 and 19).